Regularity of Weak Solution of Variational Problems Modeling the Cosserat Micropolar Elasticity

Regularity Criterion for Weak Solution to the 3D Micropolar Fluid Equations

Strong Topological Regularity and Weak Regularity of Banach Algebras

In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...

Numerical solution of variational problems via Haar wavelet quasilinearization technique

In this paper, a numerical solution based on Haar wavelet quasilinearization (HWQ) is used for finding the solution of nonlinear Euler-Lagrange equations which arise from the problems in calculus of variations. Some examples of variational problems are given and outcomes compared with exact solutions to demonstrate the accuracy and efficiency of the method.

Weak solutions of the transmission problem in anti-plane Cosserat elasticity

The theory of Cosserat elasticity (also known as micropolar or asymmetric elasticity) was introduced by Cosserat brothers [1] and further developed by Eringen [2] to model the mechanical behavior of materials for which the microstructure is significant (see [3] for a review of works in this area and an extensive bibliography). The theory was intended to eliminate discrepancies between the class...

Regularity and Conditioning in the Variational Analysis of Solution Mappings

Concepts of conditioning have long been important in numerical work on solving systems of equations, but in recent years attempts have been made to extend them to feasibility conditions, optimality conditions, complementarity conditions and variational inequalities, all of which can be posed as solving “generalized equations” for set-valued mappings. Here, the conditioning of such generalized e...